Formal Analysis of Deep Binarized Neural Networks

Understanding properties of deep neural networks is an important challenge in deep learning. Deep learning networks are among the most successful artificial intelligence technologies that is making impact in a variety of practical applications. However, many concerns were raised about `magical' power of these networks. It is disturbing that we are really lacking of understanding of the decision making process behind this technology. Therefore, a natural question is whether we can trust decisions that neural networks make. One way to address this issue is to define properties that we want a neural network to satisfy. Verifying whether a neural network fulfills these properties sheds light on the properties of the function that it represents. In this work, we take the verification approach. Our goal is to design a framework for analysis of properties of neural networks. We start by defining a set of interesting properties to analyze. Then we focus on Binarized Neural Networks that can be represented and analyzed using well-developed means of Boolean Satisfiability and Integer Linear Programming. One of our main results is an exact representation of a binarized neural network as a Boolean formula. We also discuss how we can take advantage of the structure of neural networks in the search procedure.